Maffei told CNBC on Thursday that what Fox is doing is to recognize "that the cable networks are generally receiving higher affiliate fees than (Fox is) getting in retransmission fees. If (Fox) is particularly being tamped in retransmission fees, what is (the company's) incentive to be a broadcast network?"

"One of the questions for the long term is 'what is the role of a broadcast network?' and are there other ways to distribute that that are more efficient. I think there are a lot of questions around Aereo and how the space evolves," Maffei said in the "Squawk on the Street" interview.

Liberty Media, which has major stakes in a number of companies, including Sirius XM, QVC and Barnes and Noble, previously owned large positions in DirecTV and Starz, and has reduced or spun off its positions in both companies over the past several years. Liberty is still active in the media space and Maffei remains the chairman of Starz. This week, he was named chairman of Sirius.

"It just recognizes that we are in hard control, I don't think it's going to mean much change in the business day to day. Frankly, the fact that the consumer likes the product and is buying it, car sales are good. All those are positives," he said.

On identifying a new CEO for Sirius, Maffei said the search committee is "getting close," but he would not comment on a specific time table. He added that although the company has made "no final determination" and "no timetable," Maffei said that a spinoff of Sirius from Liberty was "absolutely" a possibility. "At some point, it might make sense for Sirius to be a totally independent, separate company."